The Cost of Trend Chasing and The Illusion of Momentum Profits

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1 The Cost of Trend Chasing and The Illusion of Momentum Profits Donald B. Keim Finance Department The Wharton School 2300 Steinberg/Dietrich Hall University of Pennsylvania Philadelphia, PA First Draft: May 28, 2003 This draft: July 29, 2003 Thanks to Mark Carhart, Bruce Grundy, Kevin Johnson, Ananth Madhavan, Andrew Metrick, David Musto and especially Ken Kavajecz for helpful discussions, and Josh Krotec and Jed Nussdorf for excellent research assistance. Thanks also to the Plexus Group for generously providing the data. Financial support from the Institute for Quantitative Research in Finance and the Morgan Stanley Equity Market Microstructure Research Grant Program is gratefully acknowledged. All errors are mine.

2 The Cost of Trend Chasing and The Illusion of Momentum Profits Abstract There is a large and growing literature documenting the relation between ex ante observable variables and stock returns. Importantly, much of the evidence on the relation between returns and observable variables like market capitalization, the ratio of price/book, and prior price change has been portrayed in the context of returns to simulated portfolio strategies. Often missing in these analyses is the distinction between realizable returns (i.e., the returns portfolio managers can realistically achieve in practice) and returns to simulated strategies. There is ample evidence that size and value strategies can be successfully implemented in practice; that is not the case for momentum strategies. This paper documents the costs of implementing actual momentum strategies. I examine the trade behavior, and the costs of those trades, for three distinct investor styles (momentum, fundamental/value, and diversified/index) for 33 institutional investment managers executing trades in the U.S. and 36 other equity markets worldwide in both developed and emerging economies. The results show: (1) that momentum traders do indeed condition their trades on prior price movements; and (2) that costs for trades that are made conditional on prior market returns are significantly greater than for unconditional costs, especially for momentum traders. The evidence that we report on the actual costs of momentum-based trades indicates that the returns reported in previous studies of simulated momentum strategies are not sufficient to cover the costs of implementing those strategies.

3 The Cost of Trend Chasing and The Illusion of Momentum Profits 1. Introduction There is a large and growing literature documenting the relation between stock returns and observable variables like market capitalization, the ratio of price to book, and prior price changes. Importantly, much of the evidence on this relation has been portrayed in the context of returns to simulated portfolio strategies. Often missing in the analyses of simulated portfolio strategies is the distinction between simulated paper returns and realizable returns (investment strategy returns net of the costs of implementing the strategy). There is ample evidence that size and value strategies can be successfully implemented in practice; 1 that is not obviously the case for momentum strategies. The paper profits generated by simulated momentum strategies appear, to many researchers, to be inconsistent with the Efficient Markets Hypothesis. 2 However, to violate the Efficient Markets Hypothesis abnormal returns must exceed the costs of implementing the strategy designed to generate them. This paper contributes to the growing literature on momentum in stock prices by documenting the costs of implementing actual momentum strategies, and showing that costs for trades that are made conditional on past market movements are significantly greater than unconditional costs. I estimate the implementation costs of momentum strategies directly from the trades of momentum-oriented institutional investors over two different twelve-month periods during The data include trades not only for momentum managers but also for value and passive managers, and cover more than 1.6 million trades worth $1.1 trillion in the U.S. and 36 other equity markets worldwide in both developed and emerging economies. As such, they permit a more precise focus on the issues than previously possible. The paper makes three contributions. First, I investigate whether trend chasing is evident in the trading behavior of the three investment styles in the data. The results show that the momentum traders are indeed conditioning their trades on prior price movements. Estimation of 1 For example, Dimensional Fund Advisors and LSV Asset Management have developed successful mutual funds based on academic research documenting size and value effects. 2 The evidence has prompted Jegadeesh and Titman (2001) to claim that the momentum effect represents perhaps the strongest evidence against the Efficient Market Hypothesis. And Johnson (2002, JF) writes There would appear to be few more flagrant affronts to the idea of rational, efficient markets than the existence of large excess returns to simple momentum strategies in the stock market. 1

4 logit models indicate that buys are more likely to be made in rising markets and sells are more likely in falling markets for the momentum traders in my sample. This is in contrast to the index/diversified managers in the sample whose buys and sells are unrelated to recent prior price movements, and for the value managers whose buys (sells) are more likely to follow recent price declines (price increases). The findings show clear evidence of trend chasing (positive feedback trading) by the momentum traders. Second, I ask whether this trade behavior contributes in an important way to the costs of implementing the strategies. To answer the question, I separately examine the trade costs of the momentum, value and diversified traders each of whom have different motives for trading conditional on past market returns to assess how the market environment in which a trade is made affects the cost of execution (and, ultimately, the profitability of the strategy). In previous research, two different approaches have been used to gauge the profitability of momentum strategies: (1) unconditional average cost estimates from prior research are compared to the profits generated by the simulated momentum strategies (e.g., Grinblatt and Moskowitz (2002), Grundy and Martin (2001)); (2) inferences regarding price impacts are drawn from statistical models using transactions-level prices where the models are simulated without regard to the potential influence on price impacts of either the motivation for trade or the market environment in which the trade takes place and compared with the profitability of simulated momentum strategies (e.g., Korajczyk and Sadka (2002), Lesmond, Schill and Zhou (2003)). Neither of these approaches accounts for the fact that trade costs are a function of both investment style (see, e.g., Chan and Lakonishok (1995) and Keim and Madhavan (1997)) and the market conditions (e.g., a rising or a falling market) that prevail when the trade is executed. In addition, because traders often break up large trades into smaller individual trades, analysis of the price impacts of individual trades (as is necessary when using transactions-level information like that in the TAQ data base) underestimates the price impact associated with the total desired order quantity. The price impacts reported here account for all of these important factors by employing the total trade order as the unit of observation and conditioning on trade difficulty (trade size, market cap of the stock), the investment style of the manager, and the direction of the market in which the stock trades. Conditioning on past market returns is important because momentum traders are buying (selling) when the stock price is rising (falling) and the market for the stock has excess buyers (sellers). Under such conditions, their trade costs (for purchases of stocks on a rising trajectory, for 2

5 example) are expected to be higher than the unconditional average due to a combination of: (1) increased demand for liquidity on the momentum trader s side of the market due to the existence of other like-minded traders; and/or (2) reduced supply of liquidity due to fewer sellers/owners of recently appreciated stocks who don t wish to realize their capital gains. As it turns out, market environment is an important determinant of price impact. For example, one-way average price impacts for momentum traders in the U.S. are 1.21% when buying stocks in a rising market and 1.37% when selling in a falling market. Adding opportunity costs (of not being able to execute at the price prevailing at the time of the decision to trade) and commissions and other explicit costs of transacting inflates these costs to 1.82% for buys in rising markets and 1.96% for sells in falling markets. The trade costs reported here represent a clearer picture of the costs of implementing momentum strategies than previously reported in the literature and set a very high hurdle rate for the profits implied by the simulated strategies. The reality inevitably falls short of the illusion. Finally, in addition to documenting momentum trade behavior and its costs in a broad cross section of U.S. and international markets, the results also represent the first detailed analysis of the relative costs of trading equities internationally. The paper proceeds as follows. Section 2 reviews the previous evidence on momentum profits and section 3 describes the trade data used here to measure price impacts. Section 4 provides an overview of the price impacts for momentum, value and diversified traders in U.S., developed, and emerging stock markets. Section 5 reports the evidence on whether institutional trades are conditioned on prior market movements, and section 6 analyzes the conditional price impacts of momentum trades. Section 7 reports on total trade costs comprising price impacts, opportunity costs and commissions, and discusses the implications of the magnitude of these costs for the profitability of momentum strategies. Section 8 provides some evidence on the short-term performance of the momentum traders in my sample, and section 9 concludes. 2. Prior Evidence on the Profitability of Simulated Momentum Strategies The research on momentum is in general agreement that intermediate horizon (three to twelve month) stock returns exhibit significant persistence. There is little consensus, however, on the reason for persistence in returns. Some argue that its prevalence over long periods is evidence that the abnormal returns associated with momentum strategies are compensation for some unidentified source of non-diversifiable risk (Carhart (1997), Fama and French (1996)). Other research 3

6 suggests that the price momentum is related to trading in response to earnings-related news (Boni and Womack (2003), Burch and Swaminathan (2002)). Still others argue that momentum in stock prices is simply the manifestation of the trade behavior of market participants who condition trades on prior price movements (e.g., positive feedback strategies), behavior that violates the usual norms of rationality necessary for equilibrium asset pricing. Numerous investigators have attempted to model this behavior within wellestablished psychological paradigms, attributing the investor trading patterns to either underreaction (Barberis, Schleifer and Vishny (1998), Grinblatt and Han (2002)) 3 or over-reaction (Daniel, Hirshleifer and Subramanyam (1998), Hong and Stein (1999)) to the perceived information in prior price movements. Although the evidence is mixed regarding the form of the irrational behavior, this strand of research agrees that the resulting abnormal momentum profits represent a violation of the Efficient Market Hypothesis. (See footnote 2.) 2.1 The Profitability of Simulated Momentum Strategies Much of the previous research documents profits to momentum strategies simulated with CRSP data for U.S. stocks. This section briefly characterizes the magnitude of the simulated profits by surveying the original results from Jegadeesh and Titman (1993) and three additional recent studies. We also provide a brief description of the experimental strategies used to generate the profits. Jegadeesh and Titman (1993) form equal-weighted portfolios based on deciles of a ranking of all NYSE and AMEX stocks based on the prior j-month return where j is 3, 6, 9 or 12. Their analysis covers the period 1965 to The strategy buys decile 10 stocks (winners) and shorts decile 1 stocks (losers), and the profit is the net return to the long-short position, as measured over holding periods of 3, 6, 9 or 12 months. As is common to all the studies discussed below, the portfolio holding period begins one month after the creation of the portfolio to avoid microstructure-related effects in returns. The resulting monthly profits range from 0.69% to 1.49%. Note that although the list of component stocks in a portfolio does not change during the holding period, the equal weighting of the portfolios implicitly imposes a large amount of trading 3 The explanation for momentum profits in Grinblatt and Han, related to the disposition effect in which investors hold losing stocks too long and sell winning stocks too quickly, rests on capital gains and, therefore, tax considerations that apply only to taxable (individual) investors. The evidence presented in this paper indicates that a non-trivial portion of the momentum in stock prices is due to the trades of (tax-exempt) institution investors. 4

7 to the strategy as portfolios are rebalanced to equal weights every month. Profits are not adjusted for the costs of trading and portfolio turnover implicit in the strategy. Grinblatt and Moskowitz (2002) also analyze a strategy that buys decile 10 stocks (winners) and shorts decile 1 stocks (losers). Their analysis covers the period 1966 to 1995 and includes NYSE, AMEX and Nasdaq stocks.. They construct their momentum deciles by ranking stocks based on predicted returns from a multivariate regression employing a variety of lagged returns, measured over intervals of varying lengths, as independent variables (see their table 2). They construct value-weighted portfolios based on those decile breakpoints, and the profit is defined as the difference in monthly return between the top and bottom deciles. Portfolio positions are held for one month. Although their analysis includes a number of strategies resulting from several different combinations of the independent variables used in the multivariate regression, a representative strategy yields a monthly profit of 1.11%. Grinblatt and Moskowitz estimate portfolio turnover implied by this strategy to be 102.6% (monthly), and conclude that trade costs in the neighborhood of 1.0% would be sufficient to eliminate the profitability of the strategy. 4 Relying on previously published studies of trading costs (they do not measure trade costs in their paper) they conclude that the returns to their momentum strategy exceed the costs of implementation. Grundy and Martin (2001) form equal-weighted portfolios based on deciles of a ranking of all NYSE and AMEX stocks based on the prior 6-month return. Their analysis covers the period 1926 to The strategy buys decile 10 stocks (winners) and shorts decile 1 stocks (losers), and the profit is the net return to the long-short position measured over a holding period of one month. Grundy and Martin report strategy profits of 0.44% per month, and risk-adjusted profits of 1.34% per month in which the strategy s dynamic exposure to size and market factors is hedged out. Given the turnover associated with the strategy, they conclude that round-trip trade costs of 1.5% would render the strategy profits statistically insignificant. Hong, Lim and Stein (2000) form equal-weighted portfolios using a ranking of all NYSE and AMEX stocks based on the prior 6-month return. Their analysis covers the period 1980 to The strategy buys the top third of the stocks (winners) and shorts the bottom third (losers), and the profit is the net return to the long-short position measured over a holding period of six months. The resulting monthly profit from the strategy is 0.52%. The same caveat mentioned with 4 Grinblatt and Moskowitz (2002) report monthly turnover of 38.86% on the long and 63.75% on the short side of the strategy. This translates to about 450% annually for the long side and 750% on the short side. 5

8 regard to Jegadeesh and Titman about equal-weighted portfolios also applies here. Profits are not adjusted for the costs of trading and portfolio turnover implicit in the strategy. To provide some perspective, Table 1 reports momentum strategy profits as a function of portfolio turnover and total trade costs. The values across a particular row represent net profits associated with a specific level of monthly turnover while varying the level of total trade costs (price impact plus commission). Similarly, the values in a particular column represent net profits associated with a particular level of total trade cost while varying the level of monthly turnover. The values in the table are based on monthly momentum profits reported in Grinblatt and Moskowitz (2002) (GM) of 111 basis points, before adjustment for trade costs. (Although the table could be based on any unadjusted profit value, I chose the 111 basis points associated with the GM strategy because they describe it as a relatively conservative strategy that requires less trading/turnover than other simulated strategies.) Each value is defined as monthly profit (i.e., 111 basis points) minus [(monthly turnover in percent)*(trade costs in basis points)]. Monthly turnover represents roundtrip monthly turnover - for example, if during the month a portfolio manager sells 50% of the value of the positions in her portfolio, then her total trading volume during the month will be 100% of the value of her portfolio: 50% for the securities she sold and 50% for the assets bought to replace the sold positions. (Typically, turnover is stated on a one-way, as opposed to roundtrip, basis; i.e., in this case turnover would be reported as 50%.) Positive profits are in italics, losses are in bold. One could trace the curve that separates the regions of profit and loss and, thereby, identify breakeven levels of trade cost turnover combinations. For example, the strategy reported in GM has a monthly (roundtrip) turnover of 103%. If one-way total trade costs associated with that strategy were 1.05% or less, the strategy would yield positive monthly profits. It is clear from the table that profitability requires a combination of low turnover and/or low costs, characteristic that are not typical for momentum strategies. The question is whether the breakeven estimates of total trade costs reported earlier for the simulated momentum strategies are lower than the implementation costs that would be realized by actual momentum traders. Chan and Lakonishok (1995), Edwards and Wagner (1993), Keim and Madhavan (1997, 1998) and others have shown that trade costs of institutional investors vary significantly: (1) across stocks of different market capitalization and share price; (2) across different investing and trading styles; and (3) by quantity of shares traded. It is the case in the empirically simulated momentum strategies that the highest concentration of trading takes place in 6

9 stocks that are the most difficult and expensive to trade smaller cap and lower price stocks (see Lesmond, Schill and Zhou (2003)). Keim and Madhavan (1998, table 2) report average one-way total trade costs of 1.78% (2.85%) for buys and 2.03% (2.91%) for sells for the smallest cap quintile of NYSE-AMEX (Nasdaq) stocks for the period, a trading period that lies in the sample periods of the studies referenced above. Further, Keim and Madhavan (1997) show that trade costs for momentum traders in small-cap stocks are higher than for other types of traders, holding other things constant. Trade costs of this magnitude, and in combination with the high turnover rates evident in the simulated strategies (e.g., 103% for the conservative strategy in Grinblatt and Moskowitz), clearly offset the simulated profits (c.f. table 1). In recent papers, Korajczyk and Sadka (2002) and Lesmond, Schill and Zhou (2003) develop statistical models of price impacts to gauge the profitability of simulated momentum strategies. For example, Lesmond, Schill and Zhou use a variety of models to extract information about (unconditional) costs from transaction-level prices in the TAQ data. Using the resulting security-level cost estimates to calibrate the profitability of simulated momentum strategies from Jegadeesh and Titman (1993, 2001) and Hong, Lim and Stein (2000) (i.e., if the strategy is trading small cap stocks, the simulation adjusts for the costs of trading small cap stocks), they argue that the strategies are not profitable. There are several shortcomings to the analysis of price impacts in these papers. First, they don t account for the fact that traders often break up a desired order quantity into smaller trades in an attempt to soften the price impact. Thus, by measuring the price impact associated with an individual trade they are providing only a lower bound for the actual price impact associated with the total order quantity. In addition, these papers account for neither the investment style that motivates the trade nor the market environment in which the trade takes place. Momentum strategies, by their very nature, buy stocks that are rising and sell (or short sell) stocks that are dropping. In effect, the momentum trader desires to buy shares during periods of excess demand and sell during periods of excess supply. 5 Thus, to accurately measure the costs of implementing a momentum strategy one has to condition not only on the fact that such trades desire great immediacy in typically less liquid (more expensive) stocks, but also on the fact that momentum traders wish to trade on the side of the market where there is a reduced supply of liquidity (e.g., 5 Along these same lines, Kavajecz and Odders-White argue that the trading implicit in technical trading rules (e.g., trading related to support and resistance levels and to moving average rules) is related to changes in liquidity in the limit order book. 7

10 buying when there is a relative increase in the supply of buyers and a relative decrease in the supply of sellers). In such environments, the trading associated with momentum strategies exerts pressure on prices (price impact) that will certainly be greater than the price impact implicit in unconditional costs. 3. Data The data used in this study contain information on the equity transactions of 33 institutions in the U.S. and 36 other equity markets worldwide during two different time periods April 1996 to March 1997, and the calendar year The data were provided by the Plexus Group and are similar to those previously used in Keim and Madhavan (1995, 1997) (for the period Jan 1991 to Mar 1993), Barber and Odean (2002) (Jan 1993 to Mar 1996), and Conrad, Johnson and Wahal (2001) (Oct 1994 to June 1996). The main differences from those used in the earlier papers are that the data used here are from a more recent time period and include international stock transactions (the Plexus data in the previous papers contained only U.S. stock trades.) The data identify key characteristics price, number of shares traded, and date of trade of the individual trades that comprise an expressed intention to buy or sell. Thus, individual trade prices can be aggregated to a volume-weighted price associated with the total desired order quantity. As such, the unit of observation for the analysis in this paper is the trade order, which is composed of one or (typically) more transactions. To be more specific, for each order the data include the following information: (i) the identity of the stock to be traded and the date when the trading decision was made; (ii) an indication as to whether the trade is a buy or a sell; (iii) the closing stock prices (expressed in U.S. dollars) for the fifteen trade days before the decision to trade is made, and for fifteen trade days after the order is completed; (iv) the dates and the individual components of the order released to the broker; (v) the volume-weighted average trade price, number of shares traded, and date(s) associated with the trade(s) executed by the broker within a specific order; and (vi) commissions, stamp duties, and other explicit trade fees. The database contains almost 607,000 orders (more than 1.6 million individual trades) across 37 international equity markets with a total trade value of $1.1 trillion. 8

11 Importantly, for our purposes, the data indicate the institution's investment strategy or style and, thereby, provide information regarding the motivation for the trade. Plexus identifies three types of institutional investment strategies among the traders represented in the data (the identities of the traders are not revealed). Momentum traders employ a strategy that is based primarily on capturing short-term price movements. The investment strategy associated with the Value/Fundamental traders is based on assessment of fundamental value with a decidedly longerterm perspective. Index/Diversified traders seek to mimic the returns of a particular stock index or passive strategy. Thus, the underlying investment strategy dictates the trading strategy and, thereby, motivates the classification used by Plexus. The above characteristics of the data total desired trade quantity and trade style are critical for purposes of measuring and analyzing the effects of price impact on the profitability of trading strategies. 4. The Relative Price Impacts of Trading Strategies: A First Look This section provides a first look at the level of price impacts for the three types of traders included in the sample. In addition to providing summary statistics separately for each of the trader types, I also separate the sample into three market categories: U.S. markets; Developed Markets excluding the U.S.; and Emerging Markets. The countries within each category are listed in the Appendix. Finally, because the data contain two twelve-month sample periods that are separated by 33 months, and represent two very distinct market environments, I also report results separately for the two time periods April 1996 to March 1997 (96-97) and January 2000 to December 2000 (2000). The period was characterized by generally positive returns in most of the markets contained in the sample. For example, for the March 1996-April 1997 period, the average monthly returns for the value-weighted CRSP Index, the EAFE Index and the IFC Emerging Market Index are 1.27%, 0.17% and 0.96% respectively. In contrast, world equity markets were generally down during the calendar year 2000 the average monthly returns for the same three indexes for 2000 are -0.86%, -1.17% and -3.02% respectively. 6 As described in the next subsection, the analysis in this paper abstracts from the overall market environment by subtracting the local market returns from the price impacts associated with individual institutional trades. 6 These two time periods also reflect the change in minimum tick size in U.S. markets from eighths (96-97) to pennies (2000). Although such a change in the minimum tick size has clear implications for the costs of retail trades that occur at bid or ask prices, the effect on institutional trade costs (and, particularly, price impacts) in U.S. markets is less clear. See Goldstein and Kavajecz (2000), Jones and Lipson (2001) and Werner (2002) for discussion and evidence. 9

12 4.1 Definition of Price Impact The unit of observation here is an order, which is an aggregated expression of the trader s desired quantity of shares to be traded. Each order is composed of one or more individual trades. For a buyer-initiated order, the price impact is given by the ratio of the volume-weighted average price of the component trades in the order to the closing price on the day before trading of the order is initiated, less one. The total price impact for a seller-initiated trade is measured as the negative value of this quantity. Finally, market-adjusted price impact is computed by deducting the local market return (measured over the trading interval) from the total price impact. The analysis in this paper, spanning numerous international stock exchanges, argues for the reporting of price impacts net of the local market return. Differences in market returns across countries (and across subperiods) produce additional variation in price impacts, when computed inclusive of the local market returns, that is unrelated to the institutions trade behavior specific to the individual stock. Thus, deducting the local market return from the stock price movement during the trade interval isolates variation in idiosyncratic price movements specific to the institution s trades in those shares. 4.2 Variation in (Unconditional) Price Impacts across Time Periods Table 2 reports means and standard errors for price impacts adjusted for local market returns. The table is divided into three panels, moving from left to right, corresponding to the trades of Diversified, Value, and Momentum institutions respectively. The table is further divided, from top to bottom, into four additional panels corresponding to U.S. equity market trades, trades in developed markets excluding the U.S., emerging equity market trades, and market impacts averaged over all the markets in the data. Within each of the sub panels, mean price impacts are reported separately for the and 2000 time periods. Comparing the local-market-adjusted price impacts across time periods, holding trader style and market categories constant, the results in Table 2 do not reveal any clear-cut patterns in price impacts. For example, when averaged over all market categories (panel D), price impacts for buys of the Diversified and Value traders are larger in the 2000 period than in the period. However, the price impacts for the sells of the Value and Diversified traders do not exhibit systematic differences across the two time periods the 2000 sell impacts are higher (lower) than the price impacts for the Diversified (Value) traders. In contrast, both the buy and the sell average price impacts for the Momentum traders, when averaged over all markets, are larger in the 10

13 96-97 period than in the 2000 period. However, this pattern for the momentum trades does not hold across all market categories. Because price impacts across time periods do not display consistent patterns in Table 2, and because the results of tests in the following subsections are similar when estimated separately in the two subperiods, the analysis in subsequent sections pools the results from the two periods. One final point regarding subperiod differences: some variation in the (unconditional) average price impacts across sample periods may occur because of differences in trade difficulty (i.e., small-cap vs. large-cap stocks, large trades vs. small trades, etc.) across the sample periods. Section 6 estimates price impact models in which appropriate controls are applied for factors relating to trade difficulty, so those influences will be accounted for explicitly Variation in (Unconditional) Price Impacts across Market Categories Moving from top to bottom in table 2, the separate panels report price impacts for market categories that are roughly decreasing in liquidity: U.S.; Developed Markets excluding the U.S.; and Emerging Markets. The general impression from the table is that market-adjusted price impacts for buys are increasing with decreasing market liquidity, other things equal. For example, average price impacts for trades executed by the diversified and value traders tend to be the highest in emerging market stocks (buy impacts range from 0.52% to 1.15%) and are often two to four times the average for their trades in the U.S. markets. The price impacts of the buys of momentum traders deviate from this pattern. While the mean price impacts for trades in developed markets (excluding U.S.) are lower than the mean impacts for emerging market trades for the momentum traders, the average price impacts for the U.S. momentum trades are higher than for trades in emerging markets. In contrast, price impacts for sells by diversified, value and momentum traders in U.S. stocks tend to be larger than price impacts for sells in (non-u.s.) developed markets and emerging markets. However, differences in trade difficulty and manager ability which are not accounted for in these unconditional price impacts may well contribute to these differences. 7 Differences in mean price impacts across the two time periods might also reflect differences in the composition of the traders represented in the sample in the two periods, and/or differences in the quantity of trading by the same traders in the two subperiods. That is, different managers might reflect different skill levels, and those different skill levels might translate into significant differences in price impacts (Keim and Madhavan (1997)). 11

14 4.4 Variation in (Unconditional) Price Impacts across Trader Types Inspection of price impacts across trader types in Table 2 clearly shows (as in Keim and Madhavan (1997)) that Momentum traders have higher average price impacts than Value and Diversified traders. For example, in the bottom panel for all markets, the mean price impact for buys for the Momentum traders in (0.91%) is about three times larger than the corresponding mean price impacts for the Diversified (0.36%) and the Value traders (0.24%). In the 2000 subperiod the mean price impact of 0.64% for the Momentum trader buys is larger (though not by much) than the mean for the Diversified traders (0.60%) and the Value traders (0.57%). The difference in mean price impacts for sells between the Momentum traders and the other two trader types is even larger ranging from two to four times larger in both subperiods Motivation for Trade and Trader Behavior It is interesting that the significant differential in price impact between the momentum traders and the other traders is more pronounced for the sells than for the buys. This is related to asymmetries (or lack thereof) in the kinds of information motivating trade. Previous research finds that buys are more expensive than sells (Chan and Lakonishok (1995), Keim and Madhavan (1997)) and that traders are more patient (e.g., take longer to get into a position, break large trades into smaller pieces, use less aggressive orders, etc.) when buying than when selling (Keim and Madhavan (1995)). Keim and Madhavan (1997) argue that this difference between buys and sells is due to asymmetries in the informational motives between buying and selling there is a greater likelihood that buys are informationally motivated than sells because there are many possibly non-informational motives for selling, but there are fewer plausible liquidity motives for buying. This previously-observed difference in price impacts between buys and sells is evident for both the Diversified and the Value traders in table 2, in both subperiods. In contrast, momentum traders are conditioning both their buys and sells on the same kind of information past price behavior and, therefore, their buying and selling behavior and, consequently, the price impacts associated with that behavior are more symmetric. This is evident in the approximate equivalence of momentum price impacts for buys and sells in table 2 for trades executed in the U.S. markets, in other developed markets, and in emerging markets. 12

15 5. Are Institutional Trades Conditioned on Prior Price Movements? That the trade behavior of momentum institutions is linked to past price patterns distinguishes them from other traders whose strategies are more flexible and can be modified in response to changing market conditions. This section documents the relation between momentum trade behavior and market conditions by examining the pre-trade price behavior of the institutional trades in my sample. Specifically, I examine the pre-trade price behavior for three weeks (15 trade days) before the day of the first trade in an order. I subtract the local market return from the individual stock return to arrive at a market-adjusted or excess price change for the three weeks prior to the trade I call this PriorXRet. The results for the pre-trade price patterns are reported in Table 3 for the combined and 2000 time periods. 8 The first two columns of Table 3 report average values of PriorXRet separately for buyerand for seller-initiated trades. Note that these are averages of 15-day price changes and not average daily price changes within the 15-day window. Averaged over the entire sample (top row), PriorXRet is 0.83% before buy trades and 0.66% before sell trades. The third column reports a t-test of the difference between the two means to assess whether the idiosyncratic trading environment preceding buys differs from that for sells. Averaged over all institutions and markets, PriorXRet for both buy and sell trades is positive (but remember that we ve removed the overall market return from these means) but the t-value of 6.21 indicates that excess price changes preceding buys are significantly larger than those preceding sells. Of course, more interesting is the potential difference in the pre-trade market-adjusted price behavior across the different institutions with their correspondingly different motivations for trading. Thus, the remaining panels in Table 3 report mean values for PriorXRet separately for the diversified, value and momentum managers. Within each panel, I further separate the results by the market category within which the trade took place. The disaggregation by trade style reveals an interesting pattern of prior excess price changes. First, for the diversified/index institutions, whose trade are motivated more for liquidity and/or portfolio rebalancing consideration, the expectation is that their trades will not be predicated on pre-trade price behavior. The results confirm this prediction: when measured across all markets, the t-test of the difference in mean PriorXRet between buys and sells is indicating no significant difference. The results across 8 As for all the remaining tables in the paper, I have also computed results separately for the and 2000 periods. In all cases, the results across subperiods are not materially different so I report only aggregated results in the paper. Subperiod results are available on request. 13

16 markets tells essentially the same story: the t-value is insignificant for U.S. trades (1.29) and significant but with different signs for the other developed markets (t = -3.37) and emerging markets (t = 2.20). Second, the typical perception of a value or fundamentals-based trader is that she buys stocks whose prices are low relative to fundamentals (e.g., low Price to Book ratio) and sells when prices are high relative to the fundamentals. Although such trades are not explicitly conditioned on prior price movement, the buying and selling motives just described are indeed consistent with buying after prices have fallen and selling after prices have risen if fundamentals (e.g., Book Value) evolve more slowly over time than do prices. The pattern in pre-trade marketadjusted price movements for the Value managers in the sample is consistent with this prediction. Averaged over all markets, the mean PriorXRet of 0.17% for buys is significantly smaller than the mean of 0.94% for sells (t = ). This pattern is repeated for trades in both the U.S. exchanges (t = ), where the Value managers are indeed buying after (market-adjusted) price declines and selling after price increases, and in the other developed markets excluding the U.S. (t = ). For trades in emerging market exchanges, the difference in PriorXRet between buys and sells is also significant for the value managers. Finally, the objective of the momentum trader is to capture (short-term) persistence in return. As such, the momentum trader is explicitly conditioning her trades on prior price movements buying stocks that are on an upward trajectory and selling (or shorting) those on a downward trajectory. Thus, we expect PriorXRet for buys to be significantly larger than for sells for the momentum traders. This is precisely what we find, over all markets (t = 24.05) and in each of the separate market categories. Indeed, for the trades in the U.S. and emerging market exchanges, buys follow large market-adjusted price run-ups (e.g., PriorXRet = 2.33% for the U.S. trades) and sells follow market-adjusted price declines (PriorXRet = -0.31% for U.S. trades). Based on the results for mean pre-trade excess returns in the first three columns in Table 3 it is evident that the value and momentum manages are conditioning their trades, either implicitly or explicitly, on prior share price movements. To reinforce these inferences, I also estimate a logit model to accompany the t-tests in each of the separate rows in Table 3. The dependent variable in the logit model is an indicator variable that takes the value one if the order i is a buy and zero if it is a sell. The independent variable in the model is PriorXRet i, the three-week market-adjusted price change for the stock prior to order i. The estimated coefficients of the model are reported in 14

17 the middle two columns of Table 3, and are reported in bold if they are significant at the 5% level. The results of the logit estimation are consistent with the t-tests of the difference in means. For example, the significant slope coefficient of for the trades of the value institutions across all markets indicates that the higher the pre-trade market-adjusted price change, the more likely it is that a value manager s trade will be a sell. The significant slope coefficient of for the trades of the momentum traders across all markets indicates that the higher the pre-trade excess return, the more likely it is that a momentum trade will be a buy. 6. The Price Impact of Momentum Trading The previous section demonstrates that the momentum trader s raison d être chasing price trends distinguishes the behavior of momentum traders from the diversified and value traders. That their motivation for trade is indelibly linked to the trajectory of the market has two effects on the relative costs of momentum versus other types of trading. First, the momentum trader is typically chasing short-term price movements, so she demands a great deal of immediacy when trading she wants the trade executed now. Previous research has shown that increased demand for immediacy (e.g., using more aggressive market orders than more passive limit orders) results in higher trade costs (Keim and Madhavan (1997)). Second, she tends to buy in rising markets and sell in falling markets. Whereas value traders, whose objective is to buy stocks that have been depressed to price levels at or below fundamentals, are effectively paddling with the current, momentum traders are paddling against the current. It is this second effect the market environment in which the trade takes place that can result in large differences in the price impacts between the momentum traders and the others. Given that momentum traders condition their trades on prior price movements, this section examines price impacts of trades conditional on the direction of the local market in which the stock trades. We predict buys in rising markets to be more expensive (have larger price impacts) than buys in falling markets. This is because, information considerations aside, there is excess demand for the stock in rising markets due to a combination of (1) increased demand for liquidity on the momentum trader s side of the market due to the existence of other like-minded traders, and/or (2) reduced supply of liquidity due to fewer sellers/owners of recently appreciated stocks who don t wish to realize their capital gains. Thus, buyers demanding immediacy in rising markets should expect to pay a larger price concession than in falling markets, where the buyer is effectively 15

18 supplying liquidity to the market. Similar reasoning predicts that sells in falling markets will be more expensive (have larger price impacts) than sells in rising markets. To this end, Table 4 reports mean price impacts separately for buys and sells for each of the three institutional classifications and for each of the three market categories, but also reports results separately for trades occurring in rising and falling markets. A rising or falling market is determined by the three-week pre-trade return on the local stock market index being greater than zero or less than or equal to zero. Panel A contains summary statistics related to buy transactions. The first column contains information for buys executed in a falling market and the second column for buy trades executed in a rising market. Each triad contains the mean price impact (as defined in section 4.1) of the orders, the total value of the orders in billions of dollars, and the number of orders for that particular category of trade. For example, the mean price impact for buys in a rising market, across all institutions and market categories, is 0.61% based on 161,707 orders valued at $273.0 billion. The corresponding mean price impact for buys in a falling market is 0.48% (n = 166,119; $293.5 billion) which is economically and statistically significantly lower than the price impact for buys in rising markets (difference = 0.13%, t = 10.30), consistent with the above prediction. Although this pattern of buys being more expensive in rising than in falling markets holds uniformly across all institutions and market categories (the t-values in the third column reject a difference of zero in all cases), it is especially pronounced for the momentum traders. Averaged across all markets, the difference in price impacts between rising and falling markets for the momentum traders is 0.20%; the average price impact for the buys executed in rising markets is 0.84%. In comparison, the difference in price impacts between rising and falling markets for the diversified and value managers is on the order of 0.10% (averaged over all markets); and the average price impact for buys in rising markets ranges from 0.47% to 0.55% for those traders. A similar pattern emerges for the price impacts for the sell transactions in Panel B in Table 4. For example, the average price impact for sells in a falling market is 0.46%; 9 in contrast, the mean price impact for sells in a rising market is 0.22% which is economically and statistically lower than the price impact for sells in falling markets (difference = 0.24%; t = ). This significant difference is consistent with our earlier prediction. Analogous to the results for buys in Panel A, the pattern of sells being more expensive in falling than in rising markets holds 9 Recall that the price impacts for sells are multiplied by -1.0 so they can be interpreted as costs and, thereby, directly compared to impacts estimated for buys. 16

19 consistently across all institutions and markets. Once again, the difference is large for the momentum managers. Averaged over all markets, the difference in price impacts between falling and rising markets for the momentum traders is 0.19%; the average price impacts for sells executed in falling markets is 0.78%. The corresponding difference for the diversified and value traders ranges from 0.16% to 0.34%. These differences are not dramatically different from the momentum traders. The reason is that even though the mean price impact for their sells in falling markets is half the magnitude of that for the momentum traders (ranging from 0.27% to 0.39%), their price impacts for selling in a rising market are only 10 20% of the magnitude of those costs for the momentum traders. Indeed, in two instances the diversified and value traders have negative costs when selling in rising markets. The negative costs associated with the sells in rising markets can be attributed to traders acting as liquidity suppliers. Liquidity demanders pay a price concession for demanding immediacy, whereas liquidity suppliers (e.g., market makers) are paid to provide liquidity or transaction immediacy, thereby enjoying negative costs of transacting. Indeed, such negative price impacts are associated with the trades of the diversified and the value traders whose investment strategies do not require the degree of trade immediacy that is characteristic of a momentum strategy. Diversified and value strategies permit a more patient approach to trading in which liquidity provision is possible. 6.1 A Model of Price Impacts The average price impacts in table 4 do not control for differences in trade characteristics (that proxy for trade difficulty) that have been shown in previous research to affect trade costs. Thus, in this section I estimate a model of price impacts that controls explicitly for trade difficulty (e.g., trade size, market liquidity) as well as market conditions (as captured by prior price movement of the stock being traded.) The objective is to assess whether the estimated price impact function is significantly different in rising and falling markets, as might be expected given the results presented above on mean price impacts. Specifically, I estimate a variant of the model used by Keim and Madhavan (1997) in their analysis of total trade costs. For buy transactions I estimate: PI i = β 0 + β 1 TradeSize i + β 2 (1/P i ) + β 3 ln(mcap i ) + δ 0 D B i + δ 1 TradeSize i *D B B i + δ 2 (1/P i )* D i B + δ 3 ln(mcap i )* D i where PI i is the price impact for order i, TradeSize i is the number of shares traded in order i as a percent of the total shares outstanding, P i is the price of the stock in order i, Mcap i is the market 17

20 capitalization of the stock traded in order i in billions of dollars, D B i equals one if R M 0, zero otherwise, and R M is the three-week pre-trade return on the local stock market index. Larger orders should result in higher costs, so β 1 is expected to be positive. The proportional bid-ask spread decreases with price so that β 2 is expected to be greater than zero. Market capitalization of the stock being traded is included as a proxy for liquidity, so that β 3 is expected to be less than zero. Note that for buys, the coefficients β 0 to β 3 measure the price impact function in rising markets. The coefficients δ 0 to δ 3 measure the difference in the marginal effect of the independent variables on price impact (or on the level of the intercept) between falling and rising markets. A negative value for δ 1, for example, indicates that the estimated relation (slope) between price impact and trade size is lower in falling markets than in rising markets. To maintain symmetry in interpretation of the estimated coefficients for buys and sells, when estimating the model for sells the value of D S i equals one if R M > 0, and zero otherwise. Therefore, for sells the coefficients β 0 to β 3 measure the price impact function in falling markets; and the coefficients δ 0 to δ 3 measure the difference in the marginal effects of the independent variables (or in the level of the intercept) between rising and falling markets. Thus, in both models the estimated coefficients on the nondummied variables measure the impact function for trades made in the same direction as the local market movement (i.e., buys in rising markets and sells in falling markets). Turn first to the models estimated for buys in Panel A in Table 5. The estimated coefficients are generally significant and have the expected signs: price impacts are increasing in trade size, decreasing with increasing market liquidity (as proxied by market cap), and increasing with the proportional bid-ask spread (as proxied by price inverse). Comparing across trade styles, the estimated intercepts (the unconditional base-level price impact) are clearly larger for trades by momentum traders than for diversified and value traders. And controlling for bid-ask spread and market liquidity effects, the relation between price impact and trade size for momentum trades ranges from three to four times the magnitude for trades by the other institutions. The estimated coefficients on the interacted variables for buy trades are less clear regarding differences in price impacts between rising and falling markets. The estimates reveal several interesting patterns. First, the estimates of δ 0 for the different trade styles are all negative and significant, indicating that the intercepts estimated in falling markets are smaller than those in rising markets. The estimates for δ 1 indicate that the influence of trade size on price impact is significantly dampened in falling markets for value traders. However, the significant positive 18